C₅₉×#12499 #28424608

order	15104
nilpotency class	4
isoclinism	isoclinic class of #12483
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₅₉×#12499

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#459
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₅₉
prime radical	C₂×D₈×C₅₉	D₄
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄²×C₅₉ ◁ C₈²×C₅₉ ◁ G

226 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 91
transitive degree	μ_t(G) = 7552

A minimal faithful permutation representation — 3 generators on 91 points:

(1,2,5,8)(3,9,11,16)(4,13,10,7)(6,14,15,12)(17,18,21,25)(19,22,28,31)(20,29,27,24)(23,32,30,26)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,3,10,14,5,11,4,12)(2,6,13,16,8,15,7,9);(3,11)(6,15)(9,16)(12,14)(18,22)(19,26)(20,27)(23,24)(25,31)(28,32)(29,30)

Conjugacy classes & character table

2183 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 5487);